Thick film resistor (TFR) manufacturing technology is known. Due to material and process variations, TFRs cannot be screened and fired to a desired value. To overcome this problem, the resistors are screened and fired to an initial value (R.sub.fired) than the desired value. A laser then cuts into the resistive material to increase the effective resistance to the desired value (R.sub.effective). Since the value R.sub.fired can vary, the length of the laser cut varies accordingly.
At lower frequencies the length of the laser cut is not a factor in the frequency-response of the TFR. As a result, only the final R.sub.effective is significant.
At radio frequencies, however, the length of the laser cut becomes a factor in the frequency-response of the TFR. As is known, this is because the electric field distribution in the TFR is a function of the length and geometry of the laser cut. As a result, the reactive part of the TFR's input impedance (Z.sub.in) varies with the changes in the electric field distribution.
The foregoing may be understood with reference to FIGS. 2A-2D.
In FIG. 2A there is shown an equivalent circuit of a TFR. As shown, the model consists of a resistor 203 and also a capacitor 201. Here Z.sub.in may be represented by a resistive component (associated with resistor 203) and a reactive component (associated with capacitor 201). Obviously, at lower frequencies only the resistor 203 is significant, while at RF frequencies the capacitor 201 becomes increasingly significant.
In FIG. 2B there is a table showing test values for three different TFRs, identified as Units 1-3. As shown, all units 1-3 have identical resistive values (corresponding to resistor 203 in the FIG. 2A model) of fifty (50) ohms. However, the capacitance values (corresponding to capacitor 201 in the FIG. 2A model) are not identical and vary for each unit. Note the various values of 4.1, 6.2, and 5.4 pF. It will be appreciated that at low frequencies the capacitive reactance is negligible and, as a result, units 1-3 have identical 50-ohm impedances.
In FIG. 2C there is a table showing the magnitude of Z.sub.in, or .vertline.Z.sub.in .vertline., for the RF frequency band 435-475 MHz. As shown, the impedances for units 1-3 vary significantly, from 38-44 ohms. The variation is all the more significant when it is recalled that all units had identical 50-ohm impedances at low frequencies. It will be appreciated that the variations in performance seen at the RF frequencies is due to the fact that units 1-3 have differing values of capacitance (corresponding to capacitor 201 in FIG. 2A). This, of course, is related to the fact that the laser cut in each unit 1-3 is slightly different in length and geometry.
In FIG. 2D there is a graphical representation of the table shown in FIG. 2C. Note the variations in each plot (or curve) representing the .vertline.Z.sub.in .vertline. for each unit 1-3.
As a result, it would be desirable to produce a thick film resistor capable of being compensated for these variations in impedance at RF frequencies.